A Summary on Symmetries and Conserved Quantities of Autonomous Hamiltonian Systems,

Abstract

A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplectic form and then some new kinds of non-symplectic symmetries and their conserved quantities are introduced and studied.

11 pages. The paper has been substantially shortened. The bibliography has been updated

References in corpus (2)

• Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
• Non-Noether symmetries in Hamiltonian Dynamical Systems

Cited by in corpus (5)

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• Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems
• Symmetries and gauge symmetries in multisymplectic first and second-order Lagrangian field theories: electromagnetic and gravitational fields
• The geometry of Rayleigh dissipation